A new fast numerical method for the generalized Rosen-Zener model

5 Apr 2024, 11:00
30m
Sala degli Stemmi, Scuola Normale Superiore (Pisa)

Sala degli Stemmi, Scuola Normale Superiore

Pisa

P.za dei Cavalieri, 7, 56126 Pisa PI
Contributed talk

Speaker

Stefano Pozza (Charles University)

Description

In quantum mechanics, the Rosen-Zener model represents a two-level quantum system. Its generalization to multiple degenerate sets of states leads to larger non-autonomous linear systems of ordinary differential equations (ODEs). We propose a new method for computing the solution operator of this system of ODEs. This new method is based on a recently introduced expression of the solution in terms of an infinite matrix equation, which can be efficiently approximated by combining truncation, fixed point iterations, and low-rank approximation. This expression is possible thanks to the so-called ∗-product approach for linear ODEs. In the numerical experiments, the new method’s computing time scales linearly with the model’s size. We provide a first partial explanation of this linear behavior. Joint work with Christian Bonhomme and Niel Van Buggenhout.

Presentation materials